# Chapter 15 - Worked Solutions

### to questions from the OUP text *Senior Physics -
Concepts in Context* by Walding,
Rapkins and Rossiter

My thanks to Peter Finch from St Joseph's College, Gregory Terrace, for these (pdf) solutions.

Solutions-Ch15-Finch.pdf

The rest are by Greg Rapkins:

**Q39.**

Red light - 650 nm, Orange light - 580 nm, Grating - 1000 lines/cm

The spacing between the lines = 1/1000 cm = 10^{-5}m

For the 2nd order bright fringe sin q = n l/d

For red light :

sin q = 2 x 650 x10^{-9}/10^{-5} = 0.13
q = 7.47 ^{o}

For orange light :

sin q = 2 x 580 x10^{-9} /10^{-5} = 0.166, q = 6.66 ^{o}.

**Q40.**

A maximum occurs at l = 600 nm, A minimum occurs at l = 450 nm

n = 1.33

For light going from air to soap to air (see table 15.3) less - more - less:

destructive interference occurs at 2d = m l

constructive interference occurs at 2d = (m - ½ ) l

therefore 2d = m x 450 nm, and 2d = (m - ½ ) x 600 nm

therefore 450 m = 600 m - 300

m = 2

therefore
2 d = 2 x 450 nm , d = 450 nm, and 2 d = (2 - ½ ) x 600 = 1.5 x 600

d = 450 nm, this is the wavelength in air.

l_{m} = l_{a} / n = 450 /1.33 = 338 nm

**Q41.**

Destructive inference at l = 500 nm and 700 nm

For destructive inference with light going from low - medium - higher :

2 d = ( m - ½ ) l

d = ¼ l , ¾ l , 5/4l......

for 500 nm d = 125 nm, 375 nm, 625 nm, 875 nm, ......

for 700 nm d = 175 nm, 535 nm, 875 nm, ....

the common value occurs at d = 875 nm.

But since l_{m} = l_{a} / n, and since d = 5/4 l at 700 nm in air.

In the medium the l= 700 / 1.3 = 538.5 nm

then the thickness = 5/4 x 538.5 nm = 673 nm.

Check for l= 500

l_{m} = 500/ 1.3 = 384.6 nm

d = 7/4 l = 7/4 x 384.6 nm = 673 nm.

**Q 42.**

from table 15.4 L- M - L : 2d = ( m - ½ ) l

that is : 1 x 10^{-6} m = ½ l, 3/2l, 3/2l.......

that is : l = 2 x 10^{-6} m , 6.7 x 10^{-7} m, 4 x 10^{-7} m, 2.86 x 10^{-7} m ...

this is the thickness in the medium. In air l = l_{m} x n

= 2.9 x 10^{-6}m , 9.7 x 10^{-7}m, 5.8 x 10^{-7} m, 4.14 x 10^{-7} m...

= 2900 nm, 970 nm, 580 nm, 414 nm....

from table 15.4 Indigo- violet 400 - 420 nm

and green light goes from 490 - 580 nm

therefore you will see Indigo-violet, and green light.

**Q43.**

At the apex destructive interference occurs. The first constructive interference line occurs at ¼ l of air gap between the slides. Then at 3/4l , 5/4l......

Since the paper is 5 cm from the end and the bands are 0.4 mm apart then there are 50 /0.4 or 125 gaps.

Therefore the edge of the paper is over the 124th bright band.

Since 2d = (m - ½) l

2d = (124 - ½ ) x 650 x 10^{-7}m

d = 4 x 10^{-5}m

**Q44.**

Example of answer:

1. Coat a glass slide with black paint.

2. Put 2 razor blades together and scratch them across the slide

3. Use a laser and double slit interference to measure the distance between the slits, that is the thickness of a single razor blade.

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